# The Science & Math of Model Railroads

Like most little boys, my son has been interested in trains since he was just a toddler.  However, unlike his peers, he was never fond of Thomas the Train. His interest first began upon watching The Polar Express and though his taste has evolved over the years, his fascination with real locomotives has never waned.

I believe this is due in part to the lifetime hobby of our dear friend, Albert, whom I mentioned in my post earlier this week when I wrote about the importance of adult mentors for children (see my post Mentors and Role Models).  Like my son, Albert developed an interest in trains as a young boy himself and has been collecting HO model railroads ever since.  He now has an incredible collection and with a little artistic help from his wife, he has put together an amazing display.

His collection of 12 locomotives, 250 rolling stock (cars or carriages), numerous buildings, and scenery take up the entire second story of their home in an awe-inspiring display.  Each model has been meticulously crafted, every detail attended to, in an effort to recreate working train and lumber yards.  Albert has worked tirelessly to recreate the route of the Union Pacific from Veneta to Coquille, Oregon. While his display is aesthetically pleasing, one could spend hours immersing oneself in all the work that has gone into the display, what really struck me were the train time tables pinned to the ceiling and the routes sketched on maps on clip boards.

HO is the most popular scale of model railway in the world; in North America 3.5 mm (0.1378 in) represents 1 real foot (304.8 mm); this ratio works out to about 1:87.1.  The name HO is derived from the fact that its 1:87 scale is approximately half that of O scale which was the smallest of the series of older and larger 0, 1, 2 and 3 scales introduced by Märklin around 1900.

In the past few years, Albert’s focus has turned his attention to programming his trains according to a timetable.  While this is an advanced skill, and my little guy is not even interested in this aspect of model trains (yet anyway), I love that this hobby is one that can grow with him.

There are a variety of programs available to aid railway modelers in creating and operating their layouts. Many timetable operators use stringline graphs to schedule their trains. These can be constructed using a spreadsheet such as Excel. For more information on building a model railroad timetable, I suggest a series of videos by Model Railroad Hobbyist Magazine.

Modern HO trains run on two-rail track, which is powered by Direct Current (varying the voltage applied to the rails to change the speed, and polarity to change direction), or by Digital Command Control (DCC – sending digital commands to a decoder in each locomotive).

On simple, usually temporary layouts, power is supplied by a power pack consisting of a transformer and rectifier, a rheostat or potentiometer for regulating voltage supplied to the track (and thus train speed), and a switch to control train direction.

On permanent layouts, multiple power supplies are traditionally used, with the track divided into electrically isolated sections called blocks; toggle or rotary switches (sometimes relays) are used to select which power supply controls the train in a particular block. With the advent of digital command control, block divisions are largely eliminated, as the computerized controllers can control any train anywhere on the track at any time, with minor limitations.